Unravelling quantum chaos using persistent homology
arXiv:2211.15100 · doi:10.1103/PhysRevE.107.044204
Abstract
Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a topology-preserving embedding method that allows reconstructing dynamical attractors, the topologies of which can be used to identify chaotic behaviour. Open quantum systems can similarly exhibit non-trivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this work, we present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach by using single quantum trajectory unravelings of the master equation to construct analogue 'quantum attractors' and extracting their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phase using limited measurements of the system.
arXiv comment9 pages, 8 figures
References in corpus (32)
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
- Characterizing Quantum Supremacy in Near-Term Devices
- Measuring the scrambling of quantum information
- Observing single quantum trajectories of a superconducting qubit
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Loschmidt Echo for quantum metrology
- Continuous Quantum Measurement and the Emergence of Classical Chaos
- Quantum Chaos in the Bose-Hubbard model
- Lyapunov exponent in quantum mechanics. A phase-space approach
- Quantum chaos in open systems: a quantum state diffusion analysis
- Information Scrambling and Chaos in Open Quantum Systems
- Probing many-body quantum chaos with quantum simulators
- Persistent topological features of dynamical systems
- Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections
- Integrability vs Quantum Thermalization
- Quantum chaos and entanglement in ergodic and non-ergodic systems
- Quantum Chaos and the Correspondence Principle
- Towards quantum advantage via topological data analysis
- A Look into Chaos Detection through Topological Data Analysis
- Quantum trajectories of superconducting qubits
- Topological time-series analysis with delay-variant embedding
- Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems
- Crossover from classical to quantum behavior of Duffing oscillator through "pseudo-Lyapunov exponent"
- Photonic band structure design using persistent homology
- Lyapunov exponents of quantum trajectories beyond continuous measurements
- Controlling chaos in the quantum regime using adaptive measurements
- Morphology of three-body quantum states from machine learning
- Effect of chaos on information gain in quantum tomography
- Photon waiting time distributions: a keyhole into dissipative quantum chaos